M670_10 (Multiple Regression)

M670_10 (Multiple Regression) - 1 Multiple Regression MGMT...

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Unformatted text preview: 1 Multiple Regression MGMT 670: Business Analytics Krannert Graduate School of Management Purdue University 2 § Describe the causal relationship between a response (or dependent) variable and one or more explanatory (or independent) variables. § Used for prediction § Simple vs. Multiple Regression Regression Models 3 Linear Multiple Regression Model § Relationship between 1 dependent variable and 1 or more independent variables is a linear function. ε β β β β + + + + + = k k X X X Y ... 2 2 1 1 Population Y-intercept Random error Population slopes Dependent (response) variable Independent (explanatory) variables 4 Estimated Multiple Regression Equation § Linear Multiple Regression Model § Estimated Linear Multiple Regression Equation (Prediction equation) ε β β β β + + + + + = k k X X X Y ... 2 2 1 1 k k X b X b X b b Y + + + + = ... ˆ 2 2 1 1 5 1. Define problem or question 2. Specify model 3. Collect data 4. Do descriptive data analysis 5. Estimate unknown parameters 6. Evaluate model 7. Use model for prediction Regression Modeling Steps 6 Step 5 Estimate Unknown Parameters § Least Squares Method Find the estimates for 0, 1, …, k, which Minimize the sum of squared errors: § Computation of coefficients’ values involves matrix algebra. We will rely on computer software packages. ∑ i=1 n ( ) Y i - Y ^ i 2 = ∑ i=1 n e i 2 7 Example: Production Problem § Sample of 30 production data collected over time Note: Rows 21 – 30 are not shown. 8 Descriptive Statistics Descriptive Statistics: Production, Machines, Workers, Loaders Variable N N* Mean SE Mean StDev Minimum Production 30 0 642.60 8.34 45.70 506.00 Machines 30 0 5.700 0.199 1.088 3.000 Workers 30 0 25.033 0.441 2.414 19.000 Loaders 30 0 10.267 0.470 2.572 6.000 Variable Q1 Median Q3 Maximum Production 619.50 646.00 671.75 734.00 Machines 5.000 6.000 7.000 7.000 Workers 23.750 25.000 27.000 30.000 Loaders 8.000 11.000 12.000 16.000 9 Matrix Plot Production Workers Loaders Machines 6.0 4.5 3.0 30 25 20 700 600 500 15 10 5 6.0 4.5 3.0 30 25 20 Matrix Plot of Production, Machines, Workers, Loaders 10 Correlations: Production, Machines, Workers, Loaders Production Machines Workers Machines 0.576 0.001 Workers 0.498 0.162 0.005 0.394 Loaders 0.493 0.128 -0.140 0.006 0.500 0.460 Cell Contents: Pearson correlation P-Value Correlation p-value 11 Minitab Printout Regression Analysis: Production versus Machines, Workers, Loaders The regression equation is Production = 210 + 18.1 Machines + 9.46 Workers + 9.03 Loaders Predictor Coef SE Coef T P VIF Constant 210.02 54.56 3.85 0.001 Machines 18.079 4.249 4.25 0.000 1.1 Workers 9.459 1.918 4.93 0.000 1.1 Loaders 9.033 1.791 5.04 0.000 1.0 S = 24.2646 R-Sq = 74.7% R-Sq(adj) = 71.8% Analysis of Variance Source DF SS MS F P Regression 3 45271 15090 25.63 0.000 Residual Error 26 15308 589 Total 29 60579 Source DF Seq SS Machines 1 20104 Workers 1 10185 Loaders 1 14982 12 Interpretation of Estimated Coefficients...
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This note was uploaded on 10/17/2011 for the course MGMT 670 taught by Professor Tawarmalani during the Spring '11 term at Purdue.

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M670_10 (Multiple Regression) - 1 Multiple Regression MGMT...

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